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Important Formulas: Inequalities and Absolute
Below is a concise document containing important Inequalities and Absolute Value formulas and concepts for the GMAT.
Basic Inequalities
Compound Inequalities
Absolute Value
Quadratic Inequalities
Important Tips
Practice Problems
1. Solve: ∣2x-3∣<5
Solution:
2. Find the range of x where x2- 4x > 5
The document Important Formulas: Inequalities and Absolute is a part of the GMAT Course Quantitative Reasoning for GMAT.
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FAQs on Important Formulas: Inequalities and Absolute
| 1. What are basic inequalities and how are they used in mathematics? |  |
Ans.Basic inequalities are mathematical expressions that compare two values or expressions using inequality signs such as <, >, ≤, and ≥. They are used to represent a range of possible values and are fundamental in solving algebraic problems, determining limits, and analyzing functions.
| 2. How do you solve absolute value inequalities? | |
Ans.To solve absolute value inequalities, you first isolate the absolute value expression on one side of the inequality. Then, you split the inequality into two separate cases: one for the positive scenario (removing the absolute value directly) and one for the negative scenario (setting the expression inside the absolute value equal to the negative of the other side). Finally, solve each case and combine the solutions.
| 3. What are the key steps to solve quadratic inequalities? | |
Ans.The key steps to solve quadratic inequalities include: 1. Rearranging the inequality into standard form (ax^2 + bx + c < 0 or > 0). 2. Finding the roots of the corresponding quadratic equation (ax^2 + bx + c = 0). 3. Using a number line to test intervals defined by the roots to determine where the inequality holds true.
| 4. What are some important tips for solving inequalities effectively? | |
Ans.Some important tips for solving inequalities include: 1. Always perform the same operation on both sides of the inequality. 2. Remember that multiplying or dividing by a negative number reverses the inequality sign. 3. Check your solutions by substituting them back into the original inequality to ensure they satisfy the condition.
| 5. Can you provide practice problems for inequalities and their solutions? | |
Ans.Yes, practice problems can include: 1. Solve the inequality |x - 3| < 5. Solution: -2 < x < 8. 2. Solve the quadratic inequality x^2 - 5x + 6 ≥ 0. Solution: x ≤ 2 or x ≥ 3.
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Apr 20, 2026 Last updated
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